TY - GEN

T1 - On Ranking-based Tests of Independence

AU - Limnios, Myrto

AU - Clémençon, Stephan

N1 - Publisher Copyright: Copyright 2024 by the author(s).

PY - 2024

Y1 - 2024

N2 - In this paper we develop a novel nonparametric framework to test the independence of two random variables X and Y with unknown respective marginals H(dx) and G(dy) and joint distribution F(dxdy), based on Receiver Operating Characteristic (ROC) analysis and bipartite ranking. The rationale behind our approach relies on the fact that, the independence hypothesis H0 is necessarily false as soon as the optimal scoring function related to the pair of distributions (H G, F), obtained from a bipartite ranking algorithm, has a ROC curve that deviates from the main diagonal of the unit square. We consider a wide class of rank statistics encompassing many ways of deviating from the diagonal in the ROC space to build tests of independence. Beyond its great flexibility, this new method has theoretical properties that far surpass those of its competitors. Nonasymptotic bounds for the two types of testing errors are established. From an empirical perspective, the novel procedure we promote in this paper exhibits a remarkable ability to detect small departures, of various types, from the null assumption H0, even in high dimension, as supported by the numerical experiments presented here.

AB - In this paper we develop a novel nonparametric framework to test the independence of two random variables X and Y with unknown respective marginals H(dx) and G(dy) and joint distribution F(dxdy), based on Receiver Operating Characteristic (ROC) analysis and bipartite ranking. The rationale behind our approach relies on the fact that, the independence hypothesis H0 is necessarily false as soon as the optimal scoring function related to the pair of distributions (H G, F), obtained from a bipartite ranking algorithm, has a ROC curve that deviates from the main diagonal of the unit square. We consider a wide class of rank statistics encompassing many ways of deviating from the diagonal in the ROC space to build tests of independence. Beyond its great flexibility, this new method has theoretical properties that far surpass those of its competitors. Nonasymptotic bounds for the two types of testing errors are established. From an empirical perspective, the novel procedure we promote in this paper exhibits a remarkable ability to detect small departures, of various types, from the null assumption H0, even in high dimension, as supported by the numerical experiments presented here.

M3 - Article in proceedings

AN - SCOPUS:85194137713

T3 - Proceedings of Machine Learning Research

SP - 577

EP - 585

BT - Proceedings of The 27th International Conference on Artificial Intelligence and Statistics

PB - PMLR

T2 - 27th International Conference on Artificial Intelligence and Statistics, AISTATS 2024

Y2 - 2 May 2024 through 4 May 2024

ER -